ESV - 26 And they cast lots for them, and the lot fell on Matthias, and he was numbered with the eleven apostles.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
I think it's important to note, as well, that whether it was Mattias or Paul, both had seen the risen Christ, which was a requirement to become an apostle. Hence, the notion of apostlic succession is not valid.
My thoughts also Cindy Jennings
It was not a requirement to be an apostle. It was a requirement to replace the *specific* ministry and apostleship of Judas.
Acts 1: 15-26
"In those days Peter stood up among the believers... and said, “Brothers and sisters the Scripture had to be fulfilled in which the Holy Spirit spoke long ago through David concerning Judas, who served as guide for those who arrested Jesus. He was one of our number and shared in our ministry....“For,” said Peter,
“it is written in the Book of Psalms:
“ ‘May his place be deserted;
let there be no one to dwell in it,
“ ‘May another take his place of leadership.’
Therefore it is necessary to choose one of the men who have been with us the whole time the Lord Jesus was living among us, beginning from John’s baptism to the time when Jesus was taken up from us. For one of these must become a witness with us of his resurrection.”
...Then they prayed, “Lord, you know everyone’s heart. Show us which of these two you have chosen to take the place of this ministry and apostleship from which Judas turned aside to go to his own place.” Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles."
There's no apostolic succession or some imaginary 'authority' passed down like Catholics or Mormons believe, but there are other apostles in the church. (Gal 1:9, Rom 16:7, Eph 4:11, etc.)
An apostle is 'one who is sent' - like missionaries who evangelize/plant churches.